The best of ideas is hurt by uncritical acceptance and thrives on critical examination.
Interpretation
Ideas flourish under scrutiny and suffer from blind acceptance.
George Polya emphasizes the importance of critical thinking in the evaluation of ideas. Accepting ideas without question can lead to stagnation, while subjecting them to rigorous examination can enhance understanding and innovation.
In practice
During a team meeting, I reminded everyone that the best solutions come from questioning our assumptions.
Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry. [...] To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery.
If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.
To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.
Mathematics is not a spectator sport!
Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself
In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.
You must begin to trust yourself sometime. I suggest you do it now. If you do not then you will forever be looking to others to prove your own merit to you, and you will never be satisfied. You will always be asking others what to do, and at the same time, resenting those from whom you seek such aid.
Rage is a powerful energy that with diligent practice can be transformed into fierce compassion. However much we disagree with our enemies, our task is to identify with them. They too feel justified in their point of view.
And what is a man without energy? Nothing - nothing at all.
When the phone started ringing too many times, I had to take it back to what I can handle. I take my chances on a job or a person as opposed to a situation. I don't like to have a situation placed over my head.
I try to take care_x000D_ and be gentle to them._x000D_ Words and eggs must be handled with care._x000D_ Once broken they are impossible things to repair.
Of all the ways of acquiring books, writing them oneself is regarded as the most praiseworthy method. Writers are really people who write books not because they are poor, but because they are dissatisfied with the books which they could buy but do not like.
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